The first thing I would do is to stop punishing people who hire illegals since that just drives it underground but make it so that if you hire someone who is not a citizen of the Untied States then you pay a 150% tax on their wages. This would discourage the hiring of illegals since the cost would be prohibitive but lets say an employer decided to hire an illegal anyways and just paid the tax on that employee. That employer would then have to report who he was paying that tax on and then the immigration authorities would know that person is a illegal. The arrest can be made. End of story.